(NPB) # # # ACL # - () 2

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1 (2012/11/5) 1

2 (NPB) # # # ACL # - () 2

3 (NPB) # # # ACL # MLB 3

4 MLB Regular Season Standings (NPB) # # # ACL # September 29, 2012 E#: Elimination Number... that will eliminate the trailing team from winning the division.... The Elimination Number for the second place team is the Magic Number for the first place team. 4

5 (NPB) # # # ACL # group tournament 5

6 (NPB) # # # ACL # 6

7 (NPB) # # # ACL # /(4 + 1) = =9 4 7

8 (NPB) # # # ACL # A B C D E F A B C D E F ( )/(2 + 1) = =

9 (NPB) # # # ACL # 9

10 (NPB) # # # ACL # 2 10

11 (NPB) # # # ACL # 1996 SF Giants SF Chronicle Adler et al., Interfaces, 2002) Clinch Avoid Elim Team W L GB GL 1st PS 1st PS Los Angeles San Diego Colorado * * 11 7 San Francisco * * E 19 11

PS Los Angeles 78 63-21 17 17 4 1 San Diego 78 65 1 19 17 17 4 0

12 Major League Baseball (MLB) (NPB) # # # ACL # American League West Texas Central Minnesota East Tampa Bay Oakland Chiago New York Los Angels Detroit Boston Seattle Cleaveland Tronto Kansas City Baltimore National League West San Francisco Central Cincinnati East Philadelphia San Diego St. Louis Atlanta Colorado Milwaukee Florida Los Angeles Houston New York Arizona Chicago Washington Pittsburgh 12

Baltimore National League West San Francisco Central Cincinnati East Philadelphia San Diego St.

13 (NPB) # # # ACL # J (NPB) (NPB) (MLB) (NPB) (NPB) MLB NPB 13

14 (NPB) # # # ACL # (1) / (2) (3) (4) (5) (6) + () (1 ) 14

15 (NPB) (NPB) # # # ACL # /(+)

16 (NPB) # # # ACL # チーム a チーム c =

17 CS (NPB) # # # ACL # CS a c 1 c 2 c 3 d 1 d =72 17

18 CS (NPB) # # # ACL # CS a (72 + 3x) (72 3x) c 1 c (24 x) x 48 c 3 a c 1 c 3 x x 144 = 72 + (24 x) 72 + (24 x)+x = 96 x 96 x =16 18

19 CS (NPB) # # # ACL # CS a c 1 c c 3 a c i or 120 CS CS

20 (NPB) # # # ACL # i w i, l i w i /(w i + l i ) i, j g ij : 0 g =(g ij )=

21 (NPB) # # # ACL # L n i L w i, l i w i /(w i + l i ) i, j L g ij i, j L g ii =0 g ji = g ij i L j L x ij i L x ii =0 i L j L x ji g ij x ij x ji g, x n 0 0 g =(g ij )=..., x =(x ij )=

22 (NPB) # # # ACL # 0 n g x ij + x ji g ij i, j L, i < j x ii =0 i L x ij 0 i, j L, i j x ij Z i, j L, i j x (Z: ) X x X i L w i + x ij j L w i + l i + j L (x ij + x ji ) 22

23 (NPB) # # # ACL # k k +1 k =1, 2,..., n 1 a L k +1 x X max x X a subject to a a k 23

24 (NPB) # CS # # # CS # ACL # max x X α A k j L x aj subject to x aj +x ja = g aj j L w a + j Lx aj w a +l a + j L g aj w i + j Lx ij w i +l i + j L (x ij +x ji ) +α i i L, i a A k α i = n k 1, α i {0,1} i L, i a i L i a 24

25 (NPB) # # # ACL # No Yes x aj j L No k +1 Yes x aj < g aj No j L j L Yes j L x aj +1 k 0 25 j L x aj k +1

26 MLB vs NPB (NPB) # # # ACL # MLB NPB QCLP 1 n n 2 n n 2 n 2 (g ij +1)(g ij +2) (g ij +1) 2 i<j one-game playoff i<j 26

27 (NPB) # # # ACL # k +1 k k =1, 2,..., n 1 a L k x X max x X a subject to a a n k 27

28 (NPB) # # # ACL # 0 k C# = k k E# = k +1 = k +1 k w w +1 k +1 k w 1 w k +1 j L g aj j L x aj 28

29 CS (NPB) # # # ACL # 29

30 CS (NPB) # # # ACL # CS ( ) 3 CS ( ) 3 2 CS CS 2 () 6 ( ) 2 ( ) 64 () =1,

31 ACL (NPB) # # # ACL # 31

32 ACL (NPB) # # # ACL # 32

33 (NPB) # # # ACL # //

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